Throughout this unit, students will gain a strong understanding of trigonometric functions, as well as how they are derived. Students will learn important terminology such as reciprocal, opposite, adjacent, and unit circle. They will understand and be able to show the relationships between the six different trigonometric functions, as well as between the different parts of a triangle. Furthermore, students will be able to derive all six functions from the unit circle. Throughout the unit, student will master the skills necessary to solve for missing lengths in a right triangle, as well as be able to recognize which trigonometric functions should be used in which context. They will also compare different ways of problem solving. Students will be able to apply their new found knowledge of trigonometric functions to real life situations. Throughout the unit, students will partake in a variety of classroom activities designed promote the growth of every student in the field Trigonometry.
Establish Goals:(G)
Maine Learning Results: Mathematics- C. Geometry
Geometric Figures
Grades 9-Diploma
3. Students understand and use basic ideas of trigonometry.
b. Use trigonometry to solve for missing lengths in right triangles.
What understandings are desired?
Students will understand that:(U)
•Trigonometry is a branch of Mathematics that deals mainly with right triangles, and the relationships between their sides and angles.
•The six trigonometric functions are essential in solving for unknowns within a right triangle.
•The unit circle is a fundamental part of Trigonometry.
What essential questions will be considered?
Essential Questions:(Q)
•How are the sides and angles of a right triangle related?
•How are the essential trigonometric functions related to each other?
•Why is the unit circle an important concept in Trigonometry?
What key knowledge and skills will students acquire as a result of this unit?
Students will know:(K)
Students will be able to do:(S)
•Important Formulas: sin, cos, tan, cot, sec, csc.
•Terminology: reciprocal, opposite, adjacent, unit circle.
•Relationships: between trigonometric functions, and
between the different parts of a triangle.
•Show the relationships between the six trigonometric functions.
•Make sense of the unit circle, and its relationship to the trigonometric functions.
•b. Use trigonometry to solve for missing lengths in right triangles.
•Compare different approaches to solving problems.
•Relate trigonometry to real-life situations.
•Recognize which trigonometric functions should be used in certain
contexts.
Performance Task
You are an architect competing to have your representation of the unit circle built at the Learning Center. The Building Committee has decided that not enough people understand the importance of trigonometry, so they are going to choose one architect to build a model of the unit circle, as well as create an informative sign to accompany the model. You will present your model in front of the committee, as well as post a blog entry on the class blog describing the unit circle, how it is formed, and how this information can be used in real world examples. The blog entries must be submitted the day before your presentation so that the committee has ample time review them before hearing your presentation. Your job is not only to explain the unit circle, and its functions, but to persuade the committee as to why your model should be the one chosen to be built in the Learning Center.
Expectations
Everyone is required to attend class. If class is missed, homework must be made up within 3 days of the class missed.
You will be graded on class participation. If you do not come to class, you do not get a grade for that day. If you have an excused absence, you may be able to do an alternative assignment to make up that grade.
All school policies are to enforced: no hats, cell phones, etc. No disrespectful behavior, no rude language. Dress code will be strictly enforced.
Student will have the opportunity after every assignment to correct their mistakes. In order to receive credit, they must schedule a time to meet with me, where we will decide together what the new grade shall be, based in the corrections. Students have up to one week to correct their assignments.
If students do not turn in homework on time, they cannot receive full credit for the assignment.
Benchmarks
Each student will be graded on a scale of 500 points. A percent will be made from these 500 points to determine the end of year grade. Point values and rubrics per assignemnt/assessment will be given to students ahead of time. I reserve the right to alter the point values of this grading system in order to provide fairness for all students.
Quizzes- 10 @ 10 points each
Quizzes will be given every week, on a Friday, except for when a project is due or when there is a test. This will include blog entries. You will know in advance which blog entries will be counted as a quiz grade. Quizzes will test your knowledge of the material covered in class since the Friday before.
Tests- 2 @ 50 points each
There will be three tests given throughout the year. They will test your knowledge of all content learned since the previos test.
Class Participation- 200 points
You are expected to participate in class. Also included in this section are any reflective journals that are written in-class. Each unexcused absence will subtract points from your total participation grade. If you have an excused absence (such as a doctor's appointment, sport's event, family emergency, etc.) then you will be given an opportunity to do a make-up assignment in order to some of the points back. This assignment will be due with the rest of your make-up work from the day(s) you missed.
Performance Task- 100 points total
You performance, as described earlier, will include a blog entry, model, and oral presentation. You model and blog entry will be counted as one grade, and your oral presentation will be counted as another grade. You will be given rubrics well in advance for you to plan accordingly.
Grading Scale
A (93-100), A- (90-92), B+ (87-89), B (83-86), B- (80-82), C+ (77-79), C (73-76), C- (70-72), D+ (67-69), D (63-66), D- (60-62), F (0-59)
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Summary of Unit
Geometric Figures
Grades 9-Diploma
3. Students understand and use basic ideas of trigonometry.
b. Use trigonometry to solve for missing lengths in right triangles.
What understandings are desired?
•The six trigonometric functions are essential in solving for unknowns within a right triangle.
•The unit circle is a fundamental part of Trigonometry.
What essential questions will be considered?
•How are the essential trigonometric functions related to each other?
•Why is the unit circle an important concept in Trigonometry?
What key knowledge and skills will students acquire as a result of this unit?
•Terminology: reciprocal, opposite, adjacent, unit circle.
•Relationships: between trigonometric functions, and
between the different parts of a triangle.
•Make sense of the unit circle, and its relationship to the trigonometric functions.
•b. Use trigonometry to solve for missing lengths in right triangles.
•Compare different approaches to solving problems.
•Relate trigonometry to real-life situations.
•Recognize which trigonometric functions should be used in certain
contexts.
Expectations
You will be graded on class participation. If you do not come to class, you do not get a grade for that day. If you have an excused absence, you may be able to do an alternative assignment to make up that grade.
All school policies are to enforced: no hats, cell phones, etc. No disrespectful behavior, no rude language. Dress code will be strictly enforced.
Student will have the opportunity after every assignment to correct their mistakes. In order to receive credit, they must schedule a time to meet with me, where we will decide together what the new grade shall be, based in the corrections. Students have up to one week to correct their assignments.
If students do not turn in homework on time, they cannot receive full credit for the assignment.
Benchmarks
Quizzes- 10 @ 10 points each
Quizzes will be given every week, on a Friday, except for when a project is due or when there is a test. This will include blog entries. You will know in advance which blog entries will be counted as a quiz grade. Quizzes will test your knowledge of the material covered in class since the Friday before.
Tests- 2 @ 50 points each
There will be three tests given throughout the year. They will test your knowledge of all content learned since the previos test.
Class Participation- 200 points
You are expected to participate in class. Also included in this section are any reflective journals that are written in-class. Each unexcused absence will subtract points from your total participation grade. If you have an excused absence (such as a doctor's appointment, sport's event, family emergency, etc.) then you will be given an opportunity to do a make-up assignment in order to some of the points back. This assignment will be due with the rest of your make-up work from the day(s) you missed.
Performance Task- 100 points total
You performance, as described earlier, will include a blog entry, model, and oral presentation. You model and blog entry will be counted as one grade, and your oral presentation will be counted as another grade. You will be given rubrics well in advance for you to plan accordingly.
Grading Scale